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Chapter 2: Q. 2.14 (page 49)

The following data were given in a study of a group of1000subscribers to a certain magazine: In reference to the job, marital status, and education, there were 312professionals, 470married persons, 525college graduates, 42professional college graduates, 147married college graduates, 86married professionals, and 25married professional college graduates. Show that the numbers reported in the

the study must be incorrect.

Hint: Let M,W,andGdenote, respectively, the set of professionals, married persons, and college graduates. Assume that one of the 1000persons is chosen at random, and use Proposition 4.4to show that if the given numbers are correct, thenP(M∪W∪G)>1.

Short Answer

Expert verified

We haveP(M∪W∪G)>1.

Step by step solution

01

Given Information.

Marital status, and education, there were 312professionals, 470married persons, 525college graduates, 42professional college graduates, 147married college graduates,86married professionals, and25married professional college graduates.

02

Explanation.

Using the proposition 4.4given in the book, we expand the equation and find that the probability calculated on the left side turns out to be greater than1, which is not allowed, and hence, the numbers reported must be wrong.

03

Explanation.

P(M∪W∪G)=P(M)+P(W)+P(G)-P(MW)-P(WG)-P(MG)+P(MWG)=0.312+0.470+0.525-0.086-0.147-0.042+0.025=1.057>1

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Most popular questions from this chapter

A certain town with a population100,000has 3newspapers:I,II,and III.The proportions of townspeople who read these papers are as follows:

I:10percent Iand II:8percentI,IIand III:1percent

II:30percentIand III:2percent

III:5percentIIandIII:4percent

(The list tells us, for instance, that8000people read newspapers IandII)

(a)Find the number of people who read only one newspaper.

(b)How many people read at least two newspapers?

(c)IfIand IIIare morning papers and IIis an evening paper, how many people read at least one-morning paper plus an evening paper?

(d)How many people do not read any newspapers?

(e)How many people read the only one-morning paper and one evening paper?

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